Precalculus Examples

$\frac{\sin (a - b)}{\cos (a) \cos (b)}$

Step 1

Separate fractions.

$\frac{1}{\cos (b)} \cdot \frac{\sin (a - b)}{\cos (a)}$

Step 2

Rewrite $\frac{\sin (a - b)}{\cos (a)}$ as a product.

$\frac{1}{\cos (b)} (\sin (a - b) \frac{1}{\cos (a)})$

Step 3

Write $\sin (a - b)$ as a fraction with denominator $1$ .

$\frac{1}{\cos (b)} (\frac{\sin (a - b)}{1} \cdot \frac{1}{\cos (a)})$

Step 4

Simplify.

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Step 4.1

Divide $\sin (a - b)$ by $1$ .

$\frac{1}{\cos (b)} (\sin (a - b) \frac{1}{\cos (a)})$

Step 4.2

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$\frac{1}{\cos (b)} (\sin (a - b) \sec (a))$

Step 5

Convert from $\frac{1}{\cos (b)}$ to $\sec (b)$ .

$\sec (b) \sin (a - b) \sec (a)$